(
The worm checks very carefully under the bridge, fearing the worst but unable to detect the unmistakable scent of troll...
)
You're correct. The simplest explanation is an empirical one: the airflow over the upper surface
is accelerated: it's accelerated when there's camber, or an angle of attack with no camber, or when there's both. You can watch it. You can calculate it. And as a consequence there must, by Bernoulli's theorem, be a pressure difference, which causes lift.
Why is it accelerated? Well, it's much harder to explain
why fluid flows in the way it does than to watch it, or calculate it. The best I can do is suggest that you look at the trailing edge.
Because the trailing edge slopes downwards, there must be a downward component of velocity of the air just behind the trailing edge. Air doesn't vanish into nothingness, and the fluid mechanical equivalent of "what goes up must come down" kicks in: the only way the air can go down at the trailing edge is if it completes the circuit by going up at the leading edge, faster over the upper surface, down at the trailing edge, and slower under the lower surface. In other words, there must be a circulation around the wing -- which you can see leaving the wingtip as a vortex.